Methods for mapping spherical or ellipsoidal three-dimensional surfaces to two-dimensional surfaces so as to form maps thereof are well known. For example, various methods of mapping the earth's surface to a two-dimensional paper map are well known. In cartography, the most common methods of projection can be conceptually described by imagining a developable surface, which is a surface that can be made translated, i.e., made flat (two-dimensional) by cutting it along certain lines and unfolding or unrolling it. Such techniques include cylindrical projections, pseudo-cylindrical projections, conic projections, and azimuthal projections.
While no such projection is perfect, i.e., no projection can be simultaneously conformal and area-preserving, various projections do have advantages associated therewith. For example, some projections are conformal, while others are area-preserving. However, all such projections provide means by which every point on the surface of the object being mapped, e.g., the earth, is represented by a unique point on the two-dimensional or developable surface, e.g., a paper map. Further, such two-dimensional representations or maps attempt to be continuous, wherein every point thereof is generally adjacent the same points which are adjacent that point on the surface of the three-dimensional objects being mapped.
While contemporary methodology provide many means for projecting the surface of a three-dimensional sphere or ellipsoid to a two-dimensional map, no such methodology is suitable for projecting a generally arbitrary three-dimensional object onto a two-dimensional surface. More particularly, the Behrmann Cylindrical Equal-Area Projection, the Gall's Stereographic Cylindrical Projection, Peters Projection, Mercator Projection, Miller Cylindrical Projection, oblique Projection, Transverse Mercator Projection, Mollweide Projection, Eckert Projection, Robinson Projection, Sinusoidal Projection, Albers Equal Area Conic Projection, Equidistant Conic Projection, Lambert Conformal Conic Projection, Polyconic Projection, Azimuthal Equidistant Projection, Lambert Azimuthal Equal Area Projection, Orthographic Projection, and Stereographic Projection may be utilized to effect such mapping of the surface of an ellipsoid onto a two-dimensional surface, such as that of a paper map. However, none of these contemporary projections is suitable for mapping a generally arbitrary three-dimensional surface, such as that of a human heart, onto a two-dimensional surface, such as that of a paper map.
Those skilled in the art will appreciate that the mapping of a three-dimensional surface, such as a human heart, onto a two-dimensional surface, such as a paper map, will provide benefits in various different applications. For example, in medical applications, wherein it is desirable to precisely locate and map various different anatomical structures, such as organs, such mapping provides a convenient means for identifying and locating various different features of such anatomical structures, such as ducts, blood vessels, nerves, tissue types, tumors, lesions, etc.
In view of the foregoing, it would be desirable to provide methodology for projecting a generally arbitrary three-dimensional surface to a two-dimensional surface.